Name ______________________________________ Date _________________________ Period __________
Algebra 2
Equations of Circles
State the center and the radius of Circles A and B.
Center of Circle A: ____________
r  _______
Center of Circle B: ____________
r  _______
You can write an equation of a circle in a coordinate plane, if you know:

______________________________________________

______________________________________________
Standard Equation of a Circle:
________________ is the center of the circle.
_______ is the radius of the circle.
Write the standard equation for Circles A and B (Refer to the diagram above).
Circle A: __________________________________
Circle B: __________________________________
If the center is the ______________ then the standard equation is _________________________________.
Example: Center 0,0 , r  5
__________________________________
I. Write the standard equation of the circle with the given center and radius.
x  h 2   y  k 2  r 2
1. center 0,0 , radius 2
__________________________________
2. center 0,1 , radius 2
__________________________________
3. center 2,0 , radius 3
__________________________________
4. center 3,3 , radius 4
__________________________________
5. center  4,2 , radius 3 __________________________________
6. center  3,5 , radius 5 __________________________________
Algebra 2
Page 1
II. Give the center and radius of the circle.
7. x 2   y  4   9
8. x  5  y 2  16
2
2
Center = _________
Center = _________
r  _______
r  _______
9. x  1   y  1  4
2
10. x  2   y  4  16
2
2
2
Center = _________
Center = _________
r  _______
r  _______
11.  x  4    y  2   25
2
12. x 2  y 2  25
2
Center = _________
Center = _________
r  _______
r  _______
III. Give the coordinates of the center, the radius, and the equation of the circle.
13.
14.
15.
Center = _________
Center = _________
Center = _________
r  _______
r  _______
r  _______
_____________________
_____________________
_____________________
IV. Match the equation of a circle with its description.
______ 16. x 2  y 2  4
A. Center  1,4 , Radius 4
______ 17. x 2  y 2  9
B. Center  2,3 , Radius 3
______ 18.  x  1   y  4   16
C. Center 0,0 , Radius 2
______ 19. x  2   y  3  9
D. Center 2,5 , Radius 3
______ 20. x  3   y  5  16
E. Center  3,5 , Radius 4
______ 21. x  2    y  5  9
F. Center 0,0 , Radius 3
2
2
2
2
Algebra 2
2
2
2
2
Page 2
To graph a circle on a coordinate plane:
1. ____________________________________________________________________________________
2. ____________________________________________________________________________________
3. ____________________________________________________________________________________
4. ____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
5. ____________________________________________________________________________________
V. Graph each circle. Label its center, and state its radius.
22. x 2  y 2  49
23. x  2   y  3  9
2
2
24. x  3   y  5  16
2
2
Center = _________
Center = _________
Center = _________
r  _______
r  _______
r  _______
Algebra 2
Page 3